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A relaxed splitting method for solving variational inclusion and fixed point problems

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Abstract

In this work, we propose an iterative method for finding a common solution of a variational inclusion problem involving a maximally monotone operator and a fixed point problem for a pseudocontractive mapping in real Hilbert space. Under some standard and easy-to-verify conditions, we establish that the sequence generated by the proposed method converges strongly to a solution of the considered problem. Numerical illustrations and application in image recovery suggest that the proposed method is easy to implement and efficient.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2024 Grant number FRB670073/0164. The first author was supported by Petchra Pra Jom Klao Master’s Degree Scholarship from King Mongkut’s University of Technology Thonburi (Grant No. 17/2564).

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Authors and Affiliations

  1. KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Kanokwan Kratuloek, Poom Kumam, Songpon Sriwongsa & Jamilu Abubarkar

  2. Department of Mathematics, Faculty of Physical and Computing Sciences, Usmanu Danfodiyo University, Sokoto, 840004, Nigeria

    Jamilu Abubarkar

  3. KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam & Songpon Sriwongsa

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  1. Kanokwan Kratuloek
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  2. Poom Kumam
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  3. Songpon Sriwongsa
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  4. Jamilu Abubarkar
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Correspondence to Poom Kumam.

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Communicated by Justin Wan.

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Kratuloek, K., Kumam, P., Sriwongsa, S. et al. A relaxed splitting method for solving variational inclusion and fixed point problems. Comp. Appl. Math. 43, 70 (2024). https://doi.org/10.1007/s40314-023-02583-5

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  • DOI: https://doi.org/10.1007/s40314-023-02583-5

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